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Runes: Armor Penetration vs. Attack Damage

Introduction

When playing an AD Carry everyone finds oneself in the position to create a cool rune setup for your carry. While most pro players switched to the AD Marks + AD Quints setup, there is still debate going on whether Arp Marks are better than the AD Marks (Everyone agrees on the AD Quints apparently). This short article is supposed to provide you with more insight on the subject and will aid the reader in making a decision on how to form one’s rune page for when playing AD Carries and other champions this dilemma applies to. What this article is not going to present is a firm conclusion that will state which one is better since there are a lot of other variables I did not take into account and for good reason. League of Legends is an incredibly volatile and dynamic game which makes it hard to work something out completely on paper. What this article will bring you, however, is a series of statements which will show you which choice is the best for a given situation.

Armor, Penetration and Damage Reduction

Before we dive into the hairy math that will be used to solve our problem, we first must get familiar how armor, armor penetration and damage reduction work. The formula that League of Legends uses is:

Here, DMGRED is the damage reduction multiplier (we are assuming no negative armor values as that is a rare case and penetration won’t influence negative armor values), A is the target’s armor (or magic resist) and P is the champion’s penetration value. P% is the percentual penetration and I’ve included it in the formula as everyone has percentual penetration with Weapon Expertise / Arcane Knowledge. H(x) is a special function known as the Heaviside Step Function and is defined like this:

This function is used so that penetration will never penetrate the armor below zero. An example graph of the total damage output (AD · DMGRED) of Caitlyn at level 3 without additional items and armor penetration marks and attack damage quintessences:

The flat line in the low armor value regions is the result of the Step Function as the armor penetration is equal or larger than the armor value; which results in, of course, dealing true damage to the target. When we are comparing two damage output functions (e.g. AD Marks vs. Arp Marks) we can easily see that there is a so-called minimum armor value and a maximum armor value. Between these values one surpasses the other. We can even already conclude that the one that surpasses between these values is the one with the lowest AD; this graph will make things clear:

The red line indicates the damage output with AD Marks while the blue line indicates the damage output with Arp Marks.

Was there a change to this because I’ve always seen every guide recommend ArP marks and commenters almost shun anyone who recommended AD marks/quints. Maybe someone wasn’t doing the math right, but ArP is what I’ve seen recommended for the past year.

people started running ad quints because its better for farming (armorpen does not increase your damage on minions) and the new armorpen mastery (10%) makes flat armorpen a little bit weaker in comparision. Another point would be ads on bot running flat armorrunes everywhere, so another little disclaimer for armorpen.

If you look at progamers runepages you will se flat ad across the board on reds. Quints people are switchin around, but the ones mostly used are AD and lifesteal (with movespeed on the rise!).

Wow. No shit. AD makes a lot more sense farming. And since I play mostly all champions that need a good farm to be any use. I’ll be giving it a shot here tonight. I have always followed the ArP marks, Arm seals, MR glyphs, ArP quint recommendation since I’ve started.